MathDB
Three conditions and number

Source:

November 21, 2005

Problem Statement

How many base 10 four-digit numbers, N=abcdN = \underline{a} \underline{b} \underline{c} \underline{d}, satisfy all three of the following conditions?
(i) 4,000N<6,000;4,000 \leq N < 6,000; (ii) NN is a multiple of 5; (iii) 3b<c63 \leq b < c \leq 6.
(A)  10(B)  18(C)  24(D)  36(E)  48 \mathbf{(A)}\; 10\qquad \mathbf{(B)}\; 18\qquad \mathbf{(C)}\; 24\qquad \mathbf{(D)}\; 36\qquad \mathbf{(E)}\; 48